Dictionary:Fig S-12

FIG. S-12.

Snell's law relations when a wave crosses a boundary between two isotropic solid media; the wave changes direction such that for either incident P-wave or S-wave,

${\displaystyle {\frac {\sin i}{V_{1}}}={\frac {\sin \theta _{p1}}{V_{p1}}}={\frac {\sin \theta _{s1}}{V_{s1}}}={\frac {\sin \theta _{p2}}{V_{p2}}}={\frac {\sin \theta _{s2}}{V_{s2}}}=p}$,

where i is the angle of the incident wave with a velocity Vi=VP1 if a P-wave or Vi=VS1 if an S-wave; ${\displaystyle \theta _{P1}}$ and ${\displaystyle \theta _{S1}}$ are the angles of reflection of the P- or S-waves in medium 1, which have velocities VP1 and VS1, respectively; ${\displaystyle \theta _{P2}}$ and ${\displaystyle \theta _{S2}}$ are the angles of refraction of the P- and S-waves in medium 2 which have velocities VP2 and VS2, respectively; p is the raypath parameter (which will be a constant along a raypath through parallel layering). If ${\displaystyle \sin _{P2}}$ or ${\displaystyle \sin _{S2}}$ exceeds 1 as given by this equation, a head wave will be generated.